Chap 1
Which allows the researcher to claim causation between an explanatory variable and a response variable?
A designed experiment allows the researcher to claim causation between an explanatory variable and a response variable
Define simple random sampling
A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.
interval level of measurement
A variable is at the interval level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning.
nominal level
A variable is at the nominal level of measurement if the values of the variable name, label, or categorize.
ordinal level
A variable is at the ordinal level of measurement if it has the properties of the nominal level of measurement, but the naming scheme allows for the values of the variable to be arranged in a ranked or specific order.
What is an observational study? What is a designed experiment? Which allows the researcher to claim causation between an explanatory variable and a response variable?
An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.
To determine customer opinion of their service, Business Depot randomly selects 150 stores during a certain week and surveys all customers present in the store. What type of sampling is used?
Cluster
What are the two requirements for a discrete probability distribution? Choose the correct answer below. Select all that apply. A. 0<P(x)<1 B. ∑P(x)=1 C. ∑P(x)=0 D. 0≤P(x)≤1
D. 0≤P(x)≤1 B. ∑P(x)=1
If a factor cannot be controlled, what should be done to reduce variability in the response variable?
Experimental units should be randomly assigned to each treatment group.
The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. A pro-free trade advocate wants to estimate the percentage of people who favor decreasing tariffs on imported goods. She conducts a nationwide survey of 1220 randomly selected adults 18 years and older. The interviewer asks the respondents, "Do you favor supporting free trade with our friendly neighbors?" (a) Which of these best describes the bias in the survey?
Response bias The interviewer should reword the question.
Explain what is meant when it is said that "data vary". How does the variability affect the results of statistical analysis?
Saying "data vary" means that the values of the variable change from individual to individual. In addition, certain variables can change over time for certain individuals. Because data vary, two different statistical analysis of the same variable can lead to different results.
To determine her body temperature, Carrie divides up her day into three parts: morning, afternoon, and evening. She then measures her body temperature at 4 randomly selected times during each part of the day. What type of sampling is used?
Stratified
Which sampling method does not require a frame?
Systematic
What makes the range less desirable than the standard deviation as a measure of dispersion?
The range does not use all the observations.
Determine whether the study depicts an observational study or an experiment. A poll is conducted by a school's English department in which sixth-grade students are asked if they prefer to be in their English class or their science class. Choose the correct description of the study.
The study is an observational study because the study examines individuals in a sample, but does not try to influence the response variable.
Determine whether the underlined value is a parameter or a statistic. The average age of men who walked on the moon is [39 years, 11 months, and 15 days]. Is the value a parameter or a statistic?
The value is a parameter because the men who walked on the moon are a population.
Determine whether the quantitative variable is discrete or continuous. Volume of water in a reservoir
The variable is continuous because it countable.
Determine whether the quantitative variable is discrete or continuous. Number of cars in a video store parking lot.
The variable is discrete because it is countable.
Determine whether the following statement is true or false. Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.
True
Suppose a surveyor wants to conduct a phone survey about a certain pizza topping. He plans to take a simple random sample. However, some people are on a do-not-call registry. Do you believe this can affect the ability of the surveyor to obtain accurate polling results? If so, how?
Yes, especially if the people who are on a do-not-call registry have a trait that is not accurately represented by the remaining people in the sample.
response variable
a variable that measures an outcome or result of a study
A polling organization contacts 1526 adult women who are 30 to 70 years of age and live in the United States and asks whether or not they had received a mammogram during the past year. What is the population in the study?
adult women who are 30 to 70 years of age and live in the United States
Case-control studies
are retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records. In case-control studies, individuals that have a certain characteristic may be matched with those who do not
A(n) _________ is a person or object that is a member of the population being studied.
individual
continuous variable
is a quantitative variable that has an infinite number of possible values that are not countable
discrete variable
is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term "countable" means that the values result from counting, such as 0, 1, 2, 3, and so on.
A(n) _______ is a numerical summary of a population.
parameter
μ
population mean
x̅
sample mean
σ
standard deviation of a population, sigma
A(n) ________is a numerical summary of a sample.
statistic
A(n) ------ is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.
stratified sample
What does it mean when a part of the population is under-represented? Choose the correct answer below.
A part of the population is under-represented when it is proportionally smaller in a sample than in its population.
ratio level
A variable is at the ratio level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning.
Researchers wanted to determine if having a Blu-ray player in the bedroom is associated with obesity. The researchers administered a questionnaire to 371 twelve-year-old adolescents. After analyzing the results, the researchers determined that the body mass index of the adolescents who had a Blu-ray player in their bedroom was significantly higher than that of the adolescents who did not have a Blu-ray player in their bedroom. Complete parts (a) through (e) below.
The researchers administered a questionnaire to obtain their data without trying to influence an explanatory variable of the study.
explanatory variable
a variable that we think explains or causes changes in the response variable
What is a designed experiment?
A designed experiment is when a researcher assigns individuals to a certain group, intentionally changing the value of an explanatory variable, and then recording the value of the response variable for each group.
Define the following terms. (a) Experimental unit (d) Factor (b) Treatment (e) Placebo (c) Response variable (f) Confounding (a) Define experimental unit. Choose the correct answer below.
A. A person, object, or some other well-defined item upon which a treatment is applied b. Any combination of the values of the factors (explanatory variables) c. The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable d. A variable whose effect on the response variable is to be assessed by the experimenter e. An innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication f. The effect of two factors (explanatory variables on the response variable) cannot be distinguished
A physician wanted to compare two types of headache relief. One type is medication and the other is using pressure points. It is a common belief that medication relieves pain faster. This belief is tested by having 10 migraine sufferers compare both types of pain relief and record their observations on a standardized scale of response. A coin flip was used to determine which type of headache relief each individual would try first. Results indicated that there was no difference in the two types of pain relief. Complete parts (a) through (f) below. (a) What type of experimental design is this? (b) What is the response variable in this study? (c) What is the factor that is set to predetermined levels? What is the treatment? (d) Identify the experimental units. Choose the correct answer below. (e) Why is a coin used to decide the headache relief each individual would try first?
a. Matched-pairs design b. The recorded observations c. The factor is the type of pain relief. The treatments are medication and using pressure points. d. The migraine sufferers e. To eliminate bias as to which pain relief was used first
Grouping together similar experimental units and then randomly assigning the experimental units within each group to a treatment is called ▼ designing blocking blinding confounding .
blocking
Cross-sectional studies
collect information about individuals at a specific point in time or over a very short period of time
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of customers arriving at a bank between noon and 1:00 P.M.. (b) The square footage of a house. (a) Is the number of customers arriving at a bank between noon and 1:00 P.M. discrete or continuous? (b) Is the square footage of a house discrete or continuous?
A. The random variable is discrete. The possible values are x=0, 1, 2,... B. The random variable is continuous. The possible values are a>0.
What does it mean if a statistic is resistant?
Extreme values (very large or small) relative to the data do not affect its value substantially.
Determine the level of measurement of the variable Monthly temperatures of 65, 70, 75, 80, 85 F
Interval
Consider the two questions shown below. (a) Out of apples, oranges, bananas, and pears, which fruit is your favorite? (b) Would you be willing to pay for social media services if your user data was your personal property that the media company could not sell? Will the order in which the questions are asked affect the survey results? If so, what can the pollster do to alleviate this response bias?
there is no obvious reason that question order would affect the survey results in this scenario.
substantial difference
use a 25% differential
Determine whether the following statement is true or false. Explain. Inferences based on voluntary response samples are generally not reliable.
True, because it is often the case that the individuals who volunteer do not accurately represent the population.
A polling organization contacts 1526 adult women who are 30 to 70 years of age and live in the United States and asks whether or not they had received a mammogram during the past year. What is the sample in the study?
The 1526 adult women who are 30 to 70 years of age and live in the United
Determine whether the study depicts an observational study or an experiment. Fifty high school students are divided into two groups. One group is shown a video on car safety. The other is not. After one week, both groups are questioned about their accident record. Is the study an observational study or an experiment?
The study is an experiment because the researchers control one variable to determine
Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of breast cancer. The researchers studied 1791 people over the course of 7 years. During this 7-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of breast cancer over the 7-year period. After their analysis, the researchers concluded that the happy individuals were less likely to experience breast cancer. Complete parts (a) through (c).
This was a cohort study cohort study, because information was collected about a group of individuals by observing them over a long period of time.
Researchers wish to know if there is a link between hypertension (high blood pressure) and consumption of salt. Past studies have indicated that the consumption of fruits offsets the negative impact of salt consumption. It is also known that there is quite a bit of person-to-person variability as far as the ability of the body to process and eliminate salt. However, no method exists for identifying individuals who have a higher ability to process salt. It is recommended that daily intake of salt should not exceed 2200 milligrams (mg). The researchers want to keep the design simple, so they choose to conduct their study using a completely randomized design. Complete parts (a) through (c). (a) What is the response variable in the study? (b) Name three factors that have been identified. Select all that apply. (c) For each factor identified, determine whether the variable can be controlled or cannot be controlled. Blood pressure ▼ can be controlled.cannot be controlled.is not a factor. Daily consumption of salt ▼ cannot be controlled.can be controlled.is not a factor. Daily consumption of fruits ▼ is not a factor.can be controlled.cannot be controlled. Body's ability to process salt ▼ can be controlled.cannot be controlled.is not a factor. Age ▼ can be controlled.is not a factor.cannot be controlled.
a. Blood pressure b. Body's ability to process salt Daily consumption of fruits Daily consumption of salt c. Blood pressure ▼ not a factor. Daily consumption of salt ▼ can be controlled. Daily consumption of fruits ▼ can be controlled. Body's ability to process salt ▼ cannot be controlled Age ▼ is not a factor d.
Researchers wanted to test the effectiveness of a new drug therapy for treating patients with strokes. To do this, they identified 120 patients with a diagnosis of strokes. Patients were randomly assigned to one of three treatment groups. Forty patients were randomly assigned to receive the new drug therapy, another 40 received the older drug therapy, and the final 40 received a placebo therapy. To measure the effectiveness of the treatment, researchers scored each patient on a standardized rating scale for strokes. After collecting and comparing the scores for the three treatment groups, the researchers concluded that the new drug therapy is significantly more effective than both the older drug therapy and the placebo therapy in the treatment of strokes. Complete parts (a) through (f). (a) What type of experimental design is this? (b) What is the population being studied? (c) What is the response variable in this study? (d) What are the treatment(s)? (e) Identify the experimental units. Choose the correct answer below.
a. Completely randomized design b. All patients with a diagnosis of strokes c. The score on the standardized rating scale for strokes d. The new drug therapy, the older drug therapy, and the placebo therapy e. the 120 patients with a diagnosis of
A cohort study
first identifies a group of individuals to participate in the study (the cohort). The cohort is then observed over a long period of time. During this time period, characteristics about the individuals are recorded and some individuals will be exposed to certain factors (not intentionally) and others will not. At the end of the study the value of the response variable is recorded for the individuals.
A news service conducted a survey of 1099 adults ages 18 years or older in a certain country, August 31−September 2, 2015. The respondents were asked, "Of every tax dollar that goes to the federal government, how many cents of each dollar would you say are wasted?" The four possible responses are that the federal government wastes less than 10 cents, between 11 cents and 25 cents, between 26 cents and 50 cents, or 51 cents or more. Of the 1099 individuals surveyed, 36% indicated that 51 cents or more is wasted. The news service reported that 36% of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 4% and a 90% level of confidence. Complete parts (a) through (e) below.
to determine the percentage of adults in the country who believe the federal government wastes 51 cents or more of every dollar
Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.41 1 0.05 2 0.28 3 0.17 4 0.09
Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive.